Step 1: Understand Bronsted-Lowry theory.\nThe Bronsted-Lowry theory defines an acid as a substance that donates a proton (H$^+$), and a base as a substance that accepts a proton.\n\n
Step 2: Analyze the given reaction.\nThe given reaction is:\n\[\text{HCl}_{(aq)} + \text{H}_2\text{O}_{(l)} \rightleftharpoons \text{H}_3\text{O}^+_{(aq)} + \text{Cl}^-_{(aq)}\]\n
Step 3: Identify proton donation and acceptance.\nIn this reaction, HCl donates a proton (H$^+$) to H$_2$O.\nTherefore, HCl acts as a Bronsted-Lowry acid.\n\n
Step 4: Identify the base.\nSince H$_2$O accepts the proton from HCl, H$_2$O acts as a Bronsted-Lowry base.\n\n
Step 5: Identify the conjugate acid and conjugate base.\nWhen H$_2$O accepts a proton, it forms H$_3$O$^+$, which is the conjugate acid of H$_2$O.\nWhen HCl donates a proton, it forms Cl$^-$, which is the conjugate base of HCl.\n\n
Step 6: Determine base$_2$.\nIn the given equation, HCl is acid$_1$ and H$_2$O is base$_2$. H$_3$O$^+$ is conjugate acid$_1$ and Cl$^-$ is conjugate base$_2$. Thus, H$_2$O is base$_2$.\n